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Parallel Lines and Transversals in Geometry

Learn the relationships between parallel lines and transversals, identify angles formed by intersecting lines, and explore properties of angles. Practice identifying parallel planes, skew lines, and angle types.

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Parallel Lines and Transversals in Geometry

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  1. Parallel Lines and Transversals Chapter 3-1

  2. Identify the relationships between two lines or two planes. • Name angles formed by a pair of lines and a transversal. • parallel lines • consecutive interior angles • alternate exterior angles • alternate interior angles • corresponding angles • parallel planes • skew lines • transversal Preparation for Standard 7.0Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key) Lesson 3-1 Ideas/Vocabulary

  3. Parallel Lines // • Two lines are // if they are coplanar and do not intersect. Triangles are used to indicate // lines

  4. Skew Lines • Lines that do not intersect but are not coplanar are called skew lines.

  5. Parallel Planes • Two planes that do not intersect.

  6. B C D A G F H E Based on looks, find a line: • // to AB and containing D •  to AB and containing D • Skew to AB and containing D • Name the plane(s) that contain D and appear to be // to plane ABE 1. DC 2. AD 4. DCH or DGH or DCG 3. DH

  7. Identify Relationships A. Name all planes that are parallel to plane AEF. Answer: plane BHG Lesson 3-1 Example 1a

  8. __ B. Name all segments that intersect AF. __ __ __ __ Answer:EF, GF, DA, and BA Identify Relationships Lesson 3-1 Example 1b

  9. __ C. Name all segments that are skew to AD. __ __ __ __ __ Answer:FG, GB, EH,EC, and CH Identify Relationships Lesson 3-1 Example 1c

  10. A • B • C • D A. Name a plane that is parallel to plane RST. plane WTZ plane SYZ plane WXY plane QRX Lesson 3-1 CYP 1a

  11. B. Name a segment that intersects YZ. A. B. C. D. XY WX QW RS Lesson 3-1 CYP 1b

  12. C. Name a segment that is parallel to RX. A. B. C. D. ZW TZ QR ST Lesson 3-1 CYP 1c

  13. D. Name a segment that is skew to TZ. __ __ __ ___ ___ RX ST XW QW • A • B • C • D Lesson 3-1 CYP 1d

  14. t 1 2 3 4 6 5 7 8 Transversal • A line that intersects two or more coplanar lines at different points. t is a transversal

  15. Identify Transversals A. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z. Lesson 3-1 Example 2a

  16. Identify Transversals B. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal. Answer: lines u, w, x,z Lesson 3-1 Example 2b

  17. Identify Transversals C. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal. Answer: lines v, x, y,z Lesson 3-1 Example 2c

  18. A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. • A • B • C • D lines c, f lines c, d, e lines c, d, f lines c, d, e, f Lesson 3-1 CYP 2a

  19. B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. • A • B • C • D no lines lines c, f lines c, d, e, f lines a, c, d, e, f Lesson 3-1 CYP 2b

  20. C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. • A • B • C • D lines a, b lines a, b, d, e, f lines a, d, f lines a, b, e Lesson 3-1 CYP 2c

  21. D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal. • A • B • C • D lines e, f lines a, b, f lines a, b, c, e, f lines a, b, c Lesson 3-1 CYP 2d

  22. t 1 2 3 4 6 5 7 8 Corresponding Angles 1 and 5 are corresponding s • Two angles that occupy corresponding positions. 2 and 6 are corresponding s 3 and 7 are corresponding s 4 and 8 are corresponding s

  23. t 1 2 3 4 6 5 7 8 Alternate Interior Angles • Two angles that lie between the two lines on opposite sides of the transversal. 3 and 6 are Alt. Int. s 4 and 5 are Alt. Int. s

  24. t 1 2 3 4 6 5 7 8 Alternate Exterior Angles • Two angles that lie outside the two lines on opposite sides of the transversal. 1 and 8 are Alt. Ext. s 2 and 7 are Alt. Ext. s

  25. t 1 2 3 4 6 5 7 8 Consecutive Interior Angles • Two angles that lie between the two lines on the same side of the transversal. 3 and 5 are Consecutive Int. s 4 and 6 are Consecutive Int. s Sometimes called Same Side Interior Angles

  26. A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: corresponding Lesson 3-1 Example 3a

  27. B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate exterior Lesson 3-1 Example 3b

  28. C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: corresponding Lesson 3-1 Example 3c

  29. D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate exterior Lesson 3-1 Example 3d

  30. E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate interior Lesson 3-1 Example 3e

  31. F. Identify 7 and 10 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: consecutive interior Lesson 3-1 Example 3f

  32. A. Identify 4 and 5. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3a

  33. B. Identify 7 and 9. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3b

  34. C. Identify 4 and 7. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3c

  35. D. Identify 2 and 11. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3d

  36. E. Identify 3 and 5. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

  37. F. Identify 6 and 9. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

  38. 9 12 10 11 2 3 1 4 7 6 8 5 Practice

  39. Homework pg. 144 12-19, 24-35, 41-44

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